scholarly journals ESTIpop: a computational tool to simulate and estimate parameters for continuous-time Markov branching processes

2020 ◽  
Vol 36 (15) ◽  
pp. 4372-4373
Author(s):  
James P Roney ◽  
Jeremy Ferlic ◽  
Franziska Michor ◽  
Thomas O McDonald
Keyword(s):  
Parameter Estimation ◽  
Continuous Time ◽  
Likelihood Function ◽  
Branching Processes ◽  
R Package ◽  
Supplementary Information ◽  
Cell Counts ◽  
The Central Limit Theorem ◽  
Multitype Branching Processes ◽  
Analytical Approaches

Abstract Summary ESTIpop is an R package designed to simulate and estimate parameters for continuous-time Markov branching processes with constant or time-dependent rates, a common model for asexually reproducing cell populations. Analytical approaches to parameter estimation quickly become intractable in complex branching processes. In ESTIpop, parameter estimation is based on a likelihood function with respect to a time series of cell counts, approximated by the Central Limit Theorem for multitype branching processes. Additionally, simulation in ESTIpop via approximation can be performed many times faster than exact simulation methods with similar results. Availability and implementation ESTIpop is available as an R package on Github (https://github.com/michorlab/estipop). Supplementary information Supplementary data are available at Bioinformatics online.

scholarly journals Efficient estimation of bounded gradient-drift diffusion models for affect on CPU and GPU

2021 ◽  
Author(s):  
Tim Loossens ◽  
Kristof Meers ◽  
Niels Vanhasbroeck ◽  
Nil Anarat ◽  
Stijn Verdonck ◽  
...  
Keyword(s):  
Parameter Estimation ◽  
Continuous Time ◽  
Graphics Processing Units ◽  
Linear Models ◽  
Likelihood Function ◽  
Efficient Estimation ◽  
Closed Form Expression ◽  
Central Processing ◽  
Research Fields ◽  
Non Linear

AbstractComputational modeling plays an important role in a gamut of research fields. In affect research, continuous-time stochastic models are becoming increasingly popular. Recently, a non-linear, continuous-time, stochastic model has been introduced for affect dynamics, called the Affective Ising Model (AIM). The drawback of non-linear models like the AIM is that they generally come with serious computational challenges for parameter estimation and related statistical analyses. The likelihood function of the AIM does not have a closed form expression. Consequently, simulation based or numerical methods have to be considered in order to evaluate the likelihood function. Additionally, the likelihood function can have multiple local minima. Consequently, a global optimization heuristic is required and such heuristics generally require a large number of likelihood function evaluations. In this paper, a Julia software package is introduced that is dedicated to fitting the AIM. The package includes an implementation of a numeric algorithm for fast computations of the likelihood function, which can be run both on graphics processing units (GPU) and central processing units (CPU). The numerical method introduced in this paper is compared to the more traditional Euler-Maruyama method for solving stochastic differential equations. Furthermore, the estimation software is tested by means of a recovery study and estimation times are reported for benchmarks that were run on several computing devices (two different GPUs and three different CPUs). According to these results, a single parameter estimation can be obtained in less than thirty seconds using a mainstream NVIDIA GPU.

scholarly journals Supercritical multitype branching processes: the ancestral types of typical individuals

2003 ◽  
Vol 35 (4) ◽  
pp. 1090-1110 ◽  
Author(s):  
Hans-Otto Georgii ◽  
Ellen Baake
Keyword(s):  
Continuous Time ◽  
Branching Processes ◽  
Almost Sure Convergence ◽  
Family Tree ◽  
Mutation Process ◽  
Convergence Theorems ◽  
Conceptual Proof ◽  
The Family ◽  
Multitype Branching Processes

For supercritical multitype Markov branching processes in continuous time, we investigate the evolution of types along those lineages that survive up to some time t. We establish almost-sure convergence theorems for both time and population averages of ancestral types (conditioned on nonextinction), and identify the mutation process describing the type evolution along typical lineages. An important tool is a representation of the family tree in terms of a suitable size-biased tree with trunk. As a by-product, this representation allows a ‘conceptual proof’ (in the sense of Kurtz et al.) of the continuous-time version of the Kesten-Stigum theorem.

Estimation for multitype branching processes

1977 ◽  
Vol 14 (04) ◽  
pp. 829-835 ◽  
Author(s):  
M. P. Quine ◽  
P. Durham
Keyword(s):  
Branching Process ◽  
Branching Processes ◽  
Natural Conditions ◽  
Multitype Branching Process ◽  
Large Samples ◽  
The Central Limit Theorem ◽  
The Matrix ◽  
Multitype Branching Processes ◽  
Branching Process With Immigration ◽  
Strongly Consistent

It is shown that certain estimators of the matrix of offspring means and the vector of stationary means in a subcritical multitype branching process with immigration are strongly consistent and obey the central limit theorem under fairly natural conditions. The results give some evidence of the robustness of the analogous autoregressive time series model in the case of large samples.

scholarly journals Conditional Distributions and Waiting Times in Multitype Branching Processes

2013 ◽  
Vol 45 (03) ◽  
pp. 692-718 ◽  
Author(s):  
H. K. Alexander
Keyword(s):  
Continuous Time ◽  
Evolutionary Biology ◽  
Branching Processes ◽  
Waiting Times ◽  
Escape Mutant ◽  
Conditional Distributions ◽  
Specific Population ◽  
Potential Applications ◽  
Population Sizes ◽  
Multitype Branching Processes

In this paper we present novel results for discrete-time and Markovian continuous-time multitype branching processes. As a population develops, we are interested in the waiting time until a particular type of interest (such as an escape mutant) appears, and in how the distribution of individuals depends on whether this type has yet appeared. Specifically, both forward and backward equations for the distribution of type-specific population sizes over time, conditioned on the nonappearance of one or more particular types, are derived. In tandem, equations for the probability that one or more particular types have not yet appeared are also derived. Brief examples illustrate numerical methods and potential applications of these results in evolutionary biology and epidemiology.

scholarly journals Conditional Distributions and Waiting Times in Multitype Branching Processes

2013 ◽  
Vol 45 (3) ◽  
pp. 692-718 ◽  
Author(s):  
H. K. Alexander
Keyword(s):  
Continuous Time ◽  
Evolutionary Biology ◽  
Branching Processes ◽  
Waiting Times ◽  
Escape Mutant ◽  
Conditional Distributions ◽  
Specific Population ◽  
Potential Applications ◽  
Population Sizes ◽  
Multitype Branching Processes

In this paper we present novel results for discrete-time and Markovian continuous-time multitype branching processes. As a population develops, we are interested in the waiting time until a particular type of interest (such as an escape mutant) appears, and in how the distribution of individuals depends on whether this type has yet appeared. Specifically, both forward and backward equations for the distribution of type-specific population sizes over time, conditioned on the nonappearance of one or more particular types, are derived. In tandem, equations for the probability that one or more particular types have not yet appeared are also derived. Brief examples illustrate numerical methods and potential applications of these results in evolutionary biology and epidemiology.

scholarly journals Supercritical multitype branching processes: the ancestral types of typical individuals

2003 ◽  
Vol 35 (04) ◽  
pp. 1090-1110 ◽  
Author(s):  
Hans-Otto Georgii ◽  
Ellen Baake
Keyword(s):  
Continuous Time ◽  
Branching Processes ◽  
Almost Sure Convergence ◽  
Family Tree ◽  
Mutation Process ◽  
Convergence Theorems ◽  
Conceptual Proof ◽  
The Family ◽  
Multitype Branching Processes

For supercritical multitype Markov branching processes in continuous time, we investigate the evolution of types along those lineages that survive up to some time t. We establish almost-sure convergence theorems for both time and population averages of ancestral types (conditioned on nonextinction), and identify the mutation process describing the type evolution along typical lineages. An important tool is a representation of the family tree in terms of a suitable size-biased tree with trunk. As a by-product, this representation allows a ‘conceptual proof’ (in the sense of Kurtz et al.) of the continuous-time version of the Kesten-Stigum theorem.

Estimation for multitype branching processes

1977 ◽  
Vol 14 (4) ◽  
pp. 829-835 ◽  
Author(s):  
M. P. Quine ◽  
P. Durham
Keyword(s):  
Branching Process ◽  
Branching Processes ◽  
Natural Conditions ◽  
Multitype Branching Process ◽  
Large Samples ◽  
The Central Limit Theorem ◽  
The Matrix ◽  
Multitype Branching Processes ◽  
Branching Process With Immigration ◽  
Strongly Consistent

It is shown that certain estimators of the matrix of offspring means and the vector of stationary means in a subcritical multitype branching process with immigration are strongly consistent and obey the central limit theorem under fairly natural conditions. The results give some evidence of the robustness of the analogous autoregressive time series model in the case of large samples.

scholarly journals DiPhiSeq: robust comparison of expression levels on RNA-Seq data with large sample sizes

2018 ◽  
Vol 35 (13) ◽  
pp. 2235-2242 ◽  
Author(s):  
Jun Li ◽  
Alicia T Lamere
Keyword(s):  
Likelihood Function ◽  
Real Data ◽  
R Package ◽  
Research Area ◽  
Supplementary Information ◽  
Control Group ◽  
Clinical Markers ◽  
Rna Seq ◽  
Expression Levels ◽  
Cancer Group

Abstract Motivation In the analysis of RNA-Seq data, detecting differentially expressed (DE) genes has been a hot research area in recent years and many methods have been proposed. DE genes show different average expression levels in different sample groups, and thus can be important biological markers. While generally very successful, these methods need to be further tailored and improved for cancerous data, which often features quite diverse expression in the samples from the cancer group, and this diversity is much larger than that in the control group. Results We propose a statistical method that can detect not only genes that show different average expressions, but also genes that show different diversities of expressions in different groups. These ‘differentially dispersed’ genes can be important clinical markers. Our method uses a redescending penalty on the quasi-likelihood function, and thus has superior robustness against outliers and other noise. Simulations and real data analysis demonstrate that DiPhiSeq outperforms existing methods in the presence of outliers, and identifies unique sets of genes. Availability and implementation DiPhiSeq is publicly available as an R package on CRAN: https://cran.r-project.org/package=DiPhiSeq. Supplementary information Supplementary data are available at Bioinformatics online.

ExperimentSubset: an R package to manage subsets of Bioconductor Experiment objects

2021 ◽  
Author(s):  
Irzam Sarfraz ◽  
Muhammad Asif ◽  
Joshua D Campbell
Keyword(s):  
Single Cell ◽  
R Package ◽  
Poor Quality ◽  
Data Matrix ◽  
Supplementary Information ◽  
Data Provenance ◽  
Rna Seq ◽  
Efficient Management ◽  
The Matrix ◽  
The Relationship

Abstract Motivation R Experiment objects such as the SummarizedExperiment or SingleCellExperiment are data containers for storing one or more matrix-like assays along with associated row and column data. These objects have been used to facilitate the storage and analysis of high-throughput genomic data generated from technologies such as single-cell RNA sequencing. One common computational task in many genomics analysis workflows is to perform subsetting of the data matrix before applying down-stream analytical methods. For example, one may need to subset the columns of the assay matrix to exclude poor-quality samples or subset the rows of the matrix to select the most variable features. Traditionally, a second object is created that contains the desired subset of assay from the original object. However, this approach is inefficient as it requires the creation of an additional object containing a copy of the original assay and leads to challenges with data provenance. Results To overcome these challenges, we developed an R package called ExperimentSubset, which is a data container that implements classes for efficient storage and streamlined retrieval of assays that have been subsetted by rows and/or columns. These classes are able to inherently provide data provenance by maintaining the relationship between the subsetted and parent assays. We demonstrate the utility of this package on a single-cell RNA-seq dataset by storing and retrieving subsets at different stages of the analysis while maintaining a lower memory footprint. Overall, the ExperimentSubset is a flexible container for the efficient management of subsets. Availability and implementation ExperimentSubset package is available at Bioconductor: https://bioconductor.org/packages/ExperimentSubset/ and Github: https://github.com/campbio/ExperimentSubset. Supplementary information Supplementary data are available at Bioinformatics online.

Sign in / Sign up

Export Citation Format

Share Document